Electricity and Magnetism for Mathematicians
eBook - PDF

Electricity and Magnetism for Mathematicians

A Guided Path from Maxwell's Equations to Yang–Mills

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Electricity and Magnetism for Mathematicians

A Guided Path from Maxwell's Equations to Yang–Mills

About this book

This text is an introduction to some of the mathematical wonders of Maxwell's equations. These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic wave, and the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell's equations. Even more surprising is that these equations and their generalizations have led to some of the most important mathematical discoveries of the past thirty years. It seems that the mathematics behind Maxwell's equations is endless. The goal of this book is to explain to mathematicians the underlying physics behind electricity and magnetism and to show their connections to mathematics. Starting with Maxwell's equations, the reader is led to such topics as the special theory of relativity, differential forms, quantum mechanics, manifolds, tangent bundles, connections, and curvature.

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Yes, you can access Electricity and Magnetism for Mathematicians by Thomas A. Garrity in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Mathematical & Computational Physics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title page
  4. Copyright information
  5. Table of contents
  6. List of symbols
  7. Acknowledgments
  8. 1 A Brief History
  9. 2 Maxwell's Equations
  10. 3 Electromagnetic Waves
  11. 4 Special Relativity
  12. 5 Mechanics and Maxwell's Equations
  13. 6 Mechanics, Lagrangians, and the Calculus of Variations
  14. 7 Potentials
  15. 8 Lagrangians and Electromagnetic Forces
  16. 9 Differential Forms
  17. 10 The Hodge Operator
  18. 11 The Electromagnetic Two-Form
  19. 12 Some Mathematics Needed for Quantum Mechanics
  20. 13 Some Quantum Mechanical Thinking
  21. 14 Quantum Mechanics of Harmonic Oscillators
  22. 15 Quantizing Maxwell's Equations
  23. 16 Manifolds
  24. 17 Vector Bundles
  25. 18 Connections
  26. 19 Curvature
  27. 20 Maxwell via Connections and Curvature
  28. 21 The Lagrangian Machine, Yang-Mills, and Other Forces
  29. Bibliography
  30. Index
  31. Color Plates